Secret-key agreement protocols over a wiretap channel controlled by two state parameters are investigated. One of the state parameters is revealed to the sender and the receiver whereas the other state parameter is revealed to the eavesdropper. A single-letter characterization of the secret-key capacity is established when no additional public discussion is permitted between the sender and the receiver. Additionally, for the case when a public discussion channel (of unlimited capacity) is available an upper bound on the secret-key capacity is provided which is tight in some special cases.